/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 37 Use synthetic division to divide... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 37

Use synthetic division to divide. \(\frac{10 x^{4}-50 x^{3}-800}{x-6}\)

Short Answer

Expert verified
The result of the synthetic division of \(10x^{4} - 50x^{3} - 800\) by \(x-6\) is \(10x^{3} + 10x^{2} + 60x + 360 + \frac{2160}{x-6}\)

Step by step solution

01

Set Up the Division

First, arrange the coefficients of the dividend polynomial, \(10x^{4} - 50x^{3} - 800\), as well as the value of x from the divisor, \(x-6\), in a line. For \(x-6\), the value of x is 6. So, you will be using 6 as the value to divide the coefficients of the dividend by. The array should look like this: 6 | 10 -50 0 0 -800.
02

Start Performing the Division

You now start the synthetic division process. Bring down the first coefficient, 10, as is. Then, multiply this 10 by x's value, 6, which gives 60. Add -50 (the second coefficient) and 60, resulting in 10. Repeat this procedure for all coefficients. For those places where the dividend polynomial has no component, use zero. After repeating this process for all coefficients, the array will look like this: 6 | 10 -50 0 0 -800 -> 10 10 60 360 2160.
03

Write Down the Result

The numbers at the bottom of your synthetic division represent the coefficients of the quotient polynomial. Starting from the second left number, the power of x decreases by one increment each time. The final number, 2160, represents the remainder term. Putting this together, the result of the division is \(10x^{3} + 10x^{2} + 60x + 360 + \frac{2160}{x-6}\)

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Determine whether each value of \(x\) is a solution of the inequality. Inequality. \(x^{2}-x-12 \geq 0 \quad\) (a) \(x=5 \quad\) (b) \(x=0\) (c) \(x=-4\) (d) \(x=-3\)

Use a graphing utility to graph the rational function. Give the domain of the function and identify any asymptotes. Then zoom out sufficiently far so that the graph appears as a line. Identify the line. \(f(x)=\frac{x^{2}+5 x+8}{x+3}\)

The formula that relates cost, revenue, and profit is _____________.

To solve a polynomial inequality, find the ______________ numbers of the polynomial, and use these numbers to create ________ __________ for the inequality.

Use a graphing utility to graph the rational function. Give the domain of the function and identify any asymptotes. Then zoom out sufficiently far so that the graph appears as a line. Identify the line. \(h(x)=\frac{12-2 x-x^{2}}{2(4+x)}\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Calculus

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.